(33s) OEIS A000966: Prohibited Zero Endings of Factorials
09-30-2017, 10:02 AM (This post was last modified: 07-23-2022 10:12 AM by Gerald H.)
Post: #1
 Gerald H Senior Member Posts: 1,627 Joined: May 2014
(33s) OEIS A000966: Prohibited Zero Endings of Factorials
[Edit 2022-07-23: Old line 5 of LBL A deleted as redundant.]

The following five programmes together produce 4 sequences from the OEIS on the HP 33s.

The 33s is a very fast calculator. The table below shows times on various HP calculators to calculate

A966(88,888,888,888)

using the programmes here presented & variously optimised for the respective calculator.

Model Time in sec
42S 45
40G 40
38G 30
35s 18
39gs 14
50g User 8.8
33s 8
49G Sys 1.2
50g Sys 0.6

The first programme takes a real integer N from the stack & returns A966(N) to stack.

https://oeis.org/A000966

Code:
1.    LBL A 2.    STO A 3.    XEQ B 4.    ENTER 5.    STO B 6.    XEQ D 7.    STO D 8.    RCL B 9.    ENTER 10.    ENTER 11.    6 12.    * 13.    -1 14.    STO Z 15.    + 16.    STO E 17.    x<>y 1.    LBL Q 2.    XEQ V 3.    STO+ E 4.    x≠0? 5.    GTO Q 6.    RCL D 7.    x≠0? 8.    GTO R 9.    RCL E 10.    RTN 1.    LBL R 2.    1 3.    STO+ Z 4.    STO- A 5.    RCL A 6.    XEQ B 7.    RCL B 8.    x=y? 9.    GTO R 10.    RCL E 11.    RCL- D 12.    RCL+ Z 13.    RTN

Takes a real integer N from the stack & returns A228297(N) to stack.

https://oeis.org/A228297

Code:
1.    LBL B 2.    ENTER 3.    ENTER 4.    XEQ V 5.    - 1.    LBL O 2.    ENTER 3.    ENTER 4.    XEQ C 5.    + 6.    x<>y 7.    R↓ 8.    x<>y 9.    - 10.    x≥0? 11.    GTO P 12.    SGN 13.    R↑ 14.    x<>y 15.    - 16.    GTO O 17.    LBL P 18.    R↑ 19.    RTN

Takes a real integer N from the stack & returns A27868(N) to stack, leaving Y, Z & T stack levels unaltered.

https://oeis.org/A027868

Code:
1.    LBL C 2.    x<>L 3.    CLx 4.    x<>L 1.    LBL N 2.    XEQ V 3.    STO+ L 4.    x≠0? 5.    GTO N 6.    x<>L 7.    RTN

Takes a real integer N from the stack & returns A112765(N) to stack.

https://oeis.org/A112765

Code:
1.    LBL D 2.    -1 1.    LBL L 2.    1 3.    + 4.    x<>y 5.    XEQ V 6.    x<>y 7.    RCL R 8.    x≠0? 9.    GTO M 10.    R↓ 11.    GTO L 1.    LBL M 2.    R↓ 3.    RTN

Takes a real integer from the stack & stores remainder on division by 5 in R & quotient in Q & returns Q to stack, leaving Y, Z & T stack levels unaltered.

Code:
1.    LBL V 2.    R↑ 3.    STO J 4.    R↓ 5.    STO R 6.    5 7.    RMDR 8.    x<>R 9.    5 10.    INT/ 11.    R↑ 12.    X<>J 13.    R↓ 14.    STO Q 15.    RTN
09-30-2017, 10:16 AM
Post: #2
 pier4r Senior Member Posts: 2,248 Joined: Nov 2014
RE: (33s) OEIS A000966: Prohibited Zero Endings of Factorials
it is nice that you got hooked on oeis sequences! They provide nice inputs.

Wikis are great, Contribute :)
07-23-2022, 10:14 AM (This post was last modified: 07-23-2022 10:15 AM by Gerald H.)
Post: #3
 Gerald H Senior Member Posts: 1,627 Joined: May 2014
RE: (33s) OEIS A000966: Prohibited Zero Endings of Factorials
In post #1 old line 5 of LBL A deleted as redundant.
04-17-2023, 05:01 AM (This post was last modified: 04-18-2023 05:09 PM by Gerald H.)
Post: #4
 Gerald H Senior Member Posts: 1,627 Joined: May 2014
RE: (33s) OEIS A000966: Prohibited Zero Endings of Factorials
[Edit: When I say "improved" I mean more elegant & smaller - unfortunately this programme takes 2* the time of the original programme.]

An improved version of programme "V":

Takes a natural number from the stack & stores remainder on division by 5 in R & quotient in Q & returns Q to stack.
Preserves stack.

Code:
1.    LBL V 2.    STO R 3.    CLx 4.    RMDR(R:5) 5.    x<>R 6.    RCL- R 7.    STO Q 8.    CLx 9.    Q/5 10.    STO Q 11.    RTN V: LN = 45
04-18-2023, 05:13 AM
Post: #5
 Steve Simpkin Senior Member Posts: 1,216 Joined: Dec 2013
RE: (33s) OEIS A000966: Prohibited Zero Endings of Factorials
(09-30-2017 10:02 AM)Gerald H Wrote:  ...
The 33s is a very fast calculator. The table below shows times on various HP calculators to calculate
...

That is really amazing considering it is using an enhanced 6502 CPU core (Sunplus SPLB31A).
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